Regensburg 2010 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 12: CE: Metal-Insulator Transition 1
TT 12.8: Vortrag
Dienstag, 23. März 2010, 11:30–11:45, H19
Real-Space Renormalization Group for Anderson Localization of Interacting Electrons in the Hubbard-Anderson Model — •Roman Katzer, Peter Henseler, and Johann Kroha — Physikalisches Institut, Universität Bonn, Germany
Anderson localization of interacting fermions remains a controversial issue even for short-range interaction. We construct a real-space renormalization group (RG) approach for the disordered Hubbard model with random onsite single-particle energies εi. The Hubbard interaction U leads to a non-trivial random distribution of many-body energy levels. In the atomic limit (hopping t → 0 adiabatically, while keeping the chemical potential equal on all sites) this distribution can be calculated exactly, depending on εi, U and the filling fraction, and can be expressed in terms of a modified (“screened”) single-particle level distribution [1]. Switching on hopping (t≠ 0), successively increasing the real-space cluster size and mapping a cluster onto a single site generates an RG flow in the space of disordered many-body Hamiltonians. Restricting the flow to low energies and observing the spin structure, the Fock space may be decimated in each RG step to keep only three Fock-space sectors with consecutive cluster occupation numbers and in each sector the lowest energy state. This leads to an RG flow of disordered Hubbard models, where the flow of the random distribution of energy levels serves as indicator for localization or delocalization. The evaluation of this scheme in d=1 agrees with previous results.
[1] P. Henseler, J. Kroha and B. Shapiro, Phys. Rev. B 77, 075101 (2008); 78, 235116 (2008).